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A194423 Numbers m such that Sum_{k=1..m} (<2/3 + k*r> - <k*r>) = 0, where r=sqrt(2) and < > denotes fractional part. 5
3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 42, 45, 48, 54, 57, 60, 66, 69, 75, 78, 81, 87, 90, 93, 99, 102, 105, 108, 111, 114, 117, 120, 123, 126, 129, 132, 135, 141, 144, 147, 153, 156, 159, 165, 168, 171, 183, 195, 240, 243, 246, 252, 255, 258, 264 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Every term is divisible by 3; see A194368.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..2043

MATHEMATICA

r = Sqrt[2]; c = 2/3;

x[n_] := Sum[FractionalPart[k*r], {k, 1, n}]

y[n_] := Sum[FractionalPart[c + k*r], {k, 1, n}]

t1 = Table[If[y[n] < x[n], 1, 0], {n, 1, 300}];

Flatten[Position[t1, 1]]         (* A194422 *)

t2 = Table[If[y[n] == x[n], 1, 0], {n, 1, 300}];

Flatten[Position[t2, 1]]         (* A194423 *)

%/3         (* A194424 *)

t3 = Table[If[y[n] > x[n], 1, 0], {n, 1, 300}];

Flatten[Position[t3, 1]]         (* A194425 *)

CROSSREFS

Cf. A194368.

Sequence in context: A194416 A036686 A329926 * A059563 A292641 A085126

Adjacent sequences:  A194420 A194421 A194422 * A194424 A194425 A194426

KEYWORD

nonn

AUTHOR

Clark Kimberling, Aug 24 2011

STATUS

approved

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Last modified October 16 03:52 EDT 2021. Contains 348035 sequences. (Running on oeis4.)